May the force be with you

You've felt it when pulling away in a quick acceleration, while cornering at high speeds and then you crash into barriers. You've even seen it in the bruises on your body. Just what are the forces exerted on the drivers of go karts?

Acceleration/Deceleration
These result when the tyres exert a forward or backward force on the track. It is the result of attempting to brake or accelerate.
This force is in the same plane as the track, below the karts centre of inertia. For this reason, the force exerts a turning moment (or torque) on the entire kart. I.e there is a downward force towards the front of the kart and an upward force at the rear of the kart while breaking and vice versa when accelerating, with the fulcrum at the center of gravity of the kart (which, is below the driver). This is called a rotational torque. There is no actual movement of any mass, but the torque effectively forces the appropriate part of the kart 'harder' down on the track.

While Cornering
While cornering, the driver feels like he is being pushed outwards from the kart. Actually, he is not being throw out but is trying to move in a straight line, due to the forward momentum. The tyres of the kart are producing a grip which imparts an angular acceleration on the kart (and driver), forcing the kart to corner. It is this angular acceleration that produces the sensation of being thrown out. The force which the ground imparts on the kart to make it corner is known as the Centripetal force, and it always acts at towards the centre of the imaginary circle we are cornering round.

Imagine the centripetal force is split into two components, a vertical and a horizontal. The horizontal force we have just described, but the vertical can be regarded as the cornering equivalent of the forward acceleration case. Because the centripetal force is acting on the kart, it imparts acceleration to it, and again, this acceleration is acting at ground level. Therefore a torque effect is again produced, but this time it is acting across the kart, and we get a weight shift to the outside of the kart. This weight shift also helps the inside wheel lift, as the weight shift reduces the weight on the inside wheel by an equivalent amount. This force has not been show on the diagram to aid clarity, but is simply in the opposite direction over the inside rear. In fact once cornering is initiated, this weight shift is more important to raising the inside wheel than the steering geometry.

The distance between the rear wheels affects how the centripetal force is distributed over the horizontal and vertical components. As the width of a track is increased, more centripetal force is distributed as a sideways force in relation to the weight shift. This means a wider track produces less weight shift to the outside rear, and more sideways force. A narrow track increases the weight shift and decreases the sideways force. Therefor a narrow track is less likely to exceed the grip of the tyres when cornering than a wide track. Consequently, the grippier the tyres used, the wider the stance can be before the grip is exceeded.

Accelerating around a corner
The final force to consider is a torque around the vertical axis experienced when accelerating during a corner. It is common knowledge that braking while cornering on a kart causes massive understeer while accelerating can improve cornering. This at first seems counterintuitive, since normally when accelerating there is a weight transfer to the rear, which you would expect to try to push the inside rear back onto the track. However, this weight transfer is dwarfed by the torque around this vertical axis caused by the fact that only one wheel rear wheel in on the track, and this wheel is offset from the centre of inertia.